1. Field of the Invention
The present invention relates to an exposure apparatus and a method of measuring Mueller Matrix of an optical system of the exposure apparatus.
2. Description of the Related Art
With increased requirements for smaller sized semiconductor integrated circuits, exposure light with a shorter wavelength is also required for an exposure apparatuses. Lasers such as an ArF excimer laser (193 nm) and an F2 laser (157 nm) come into practical use at present. For exposure light with such a shorter wavelength, the optical system often includes an optical member (such as lens) made of materials with good transmittance such as calcium fluoride (fluorite). The fluorite, however, has a large birefringence, and may generate wave-front aberration or divide the wave front in two to reduce the capability of coherency, depending on the polarization direction of the incident light. For the design of an optical system with a smaller aberration, the number of the birefringence of the optical system needs to be known.
The birefringence of a planar optical member can generally be shown by identifying the direction (azimuth) θ and phase difference Δ. This method is not suitable to express the birefringence of an optical system with a plurality of optical members having curved surfaces (such as lenses). Jones Matrix and Mueller Matrix are thus generally used to express the characteristics of the optical system having the birefringence.
Jones Matrix is a 2×2 matrix to express the optical characteristics of an optical element through which the completely-polarized light beam passes, which can be expressed by Jones Vector. Jones Vector can express the electric vector (E)=(Ex, Ey) with amplitudes ax, ay, and phase difference δ between Ex and Ey, as follows.
                    E        =                              (                                                                                E                    x                                                                                                                    E                    y                                                                        )                    =                                                    ⅇ                                  i                  ⁢                                                                          ⁢                  ω                  ⁢                                                                          ⁢                  t                                            ⁡                              (                                                                                                                              a                          x                                                ⁢                                                  ⅇ                                                      i                            ⁢                                                                                                                  ⁢                                                          φ                              x                                                                                                                                                                                                                                                        a                          y                                                ⁢                                                  ⅇ                                                      i                            ⁢                                                                                                                  ⁢                                                          φ                              y                                                                                                                                                                          )                                      =                                          ⅇ                                  i                  ⁡                                      (                                                                  ω                        ⁢                                                                                                  ⁢                        t                                            +                                              φ                        x                                                              )                                                              ⁡                              (                                                                                                    a                        x                                                                                                                                                                          a                          y                                                ⁢                                                  ⅇ                                                      i                            ⁢                                                                                                                  ⁢                            δ                                                                                                                                              )                                                                        [                  Equation          ⁢                                          ⁢          1                ]            
Jones Matrix can express the characteristics of an optical element through which the completely polarized light beam, which can be expressed by such Jones Vector, passes to undergo any conversion. For example, Jones matrix of a polarizer with azimuth θ=0 degrees can be expressed as follows.
                              P          ⁡                      (            0            )                          =                  [                                                    1                                            0                                                                    0                                            0                                              ]                                    [                  Equation          ⁢                                          ⁢          2                ]            
Jones Matrix can only handle the completely polarized light beam (including no non-polarized component) and cannot handle the partially polarized light beam including the non-polarized component. The Mueller Matrix, which can also handle the non-polarized component, is thus suitable to express the birefringence characteristics of the optical system including the fluorite lens, which certainly provides the non-polarized component. Mueller Matrix is a 4×4 matrix to express the optical characteristics of an optical element through which is passed the partially polarized light beam expressed by Stokes parameters.
With s0 being the total intensity of the light, s1 being the intensity of the 0 degrees linearly polarized component, s2 being the intensity of the 45 degrees linearly polarized component, and s3 being the intensity of the clockwise circularly polarized component, Stokes parameters can be expressed as follows, particularly for the completely polarized light beam.
                    S        =                              (                                                                                S                    0                                                                                                                    S                    1                                                                                                                    S                    2                                                                                                                    S                    3                                                                        )                    =                      (                                                                                                                              a                        x                        2                                            +                                              a                        y                        2                                                              ⁢                                                                                                                                                                                                                                a                        x                        2                                            -                                              a                        y                        2                                                              ⁢                                                                                                                                                                                  2                    ⁢                                          a                      x                                        ⁢                                          a                      y                                        ⁢                                                                                  ⁢                    cos                    ⁢                                                                                  ⁢                    δ                                                                                                                    2                    ⁢                                          a                      x                                        ⁢                                          a                      y                                        ⁢                                                                                  ⁢                    sin                    ⁢                                                                                  ⁢                    δ                                                                        )                                              [                  Equation          ⁢                                          ⁢          3                ]            
Stokes parameters express the non-polarized component with (s02−(s12+s22+s32))1/2. Stokes parameters can, thus, also express the partially polarized light beam including the non-polarized component.
Mueller Matrix can express the characteristics of an optical element through which the partially polarized light beam, which is expressed by such Stokes parameters, may pass to undergo any conversion. For example, Mueller Matrix (P0) of a polarizer with azimuth θ=0 degrees can be expressed as follows. Mueller matrix of azimuth θ is hereafter expressed by the symbol (Pθ).
                              P          0                =                              1            2                    ⁢                      (                                                            1                                                  1                                                  0                                                  0                                                                              1                                                  1                                                  0                                                  0                                                                              0                                                  0                                                  0                                                  0                                                                              0                                                  0                                                  0                                                  0                                                      )                                              [                  Equation          ⁢                                          ⁢          4                ]            
Measurement of this Mueller Matrix can facilitate the calculation about how the optical element converts the polarization state for every types of polarized light beam. One known system for measuring Mueller matrix of a single optical member is a Mueller polarimeter described in Japanese application patent laid-open publication 2000-502461 (pp. 19–22, FIGS. 1 to 4 or the like, this reference is hereafter referred to as “patent literature 1”).
The Mueller polarimeter described in the patent literature 1 or the like, however, can only measure a single optical member, and cannot measure an optical system or the like including a plurality of optical members, such as those built in an exposure apparatus or the like.
The exposure apparatuses have recently projected exposure light with a particular polarization direction for purposes such as a higher contrast of the projected pattern. For considerable birefringence or non-polarized component that occurs in the projection optical system, the birefringence or the degree of polarization must quantitatively evaluated and the resultant evaluation results must be taken into account to select the polarization direction of the exposure light. Otherwise, the desired polarization direction of the exposure light may not be provided. The characteristics of the projection optical system or the like of the exposure apparatus can be affected by aged deterioration or contamination or the like. There is, therefore, a need for measurement of Mueller matrix of the projection optical system or the like of the exposure apparatus without disassembling the exposure apparatus.